Pretty soon, on March 9, we’ll all change our clocks one hour forward to change from standard to daylight-savings time. An absolutely pure misnomer, daylight savings time is nevertheless, to my mind, the greatest success story of mass psychological control there ever has been. Just imagine if the government put out some sort of strongly worded encouragement that everyone needs to get up an hour earlier, starting Monday, and should continue to do so for the next eight months, so as to save energy and have a little more time in the evening when it’s light out. I imagine not many people would comply.

But, what they do instead is to say, “okay, starting early Sunday morning, it will suddenly be an hour later on your clock for the next eight months!” And, magically, just about everyone complies…it’s breathtaking, actually.

But what time is it really? This week, on February 29 we have a Leap Day, a once-every-four-years event. Actually, it’s not once every four years; we skip it every hundred years, except we don’t skip it every four hundred years. That is, 2000 was a leap year, but 1900, 1800, 1700 etc. were not. We’ve been doing this since 1582 when Pope Gregory introduced the new calendar to keep Easter from drifting, slowly but surely, away from the spring equinox, that magical moment when the earth’s axis makes an angle of 90 degrees to the line connecting the center of the sun with the center of the earth. On the spring equinox, the length of day and night are equal everywhere on the earth (at the poles the sun remains on the horizon all day). In the Gregorian calendar, the average calendar year is 365.2425 days, because this is the average number of days from one spring equinox to the next.

If you ask the average person on the street, though, just what “one year” means, though, they’ll most likely say “it’s the amount of time it takes the earth to go around the sun”. What they are probably thinking is that the imaginary line mentioned above from the earth to the sun sweeps out a full circle in one year; this is called a sidereal year: the time it takes for the sun to appear in the same place against the backdrop of the fixed stars. They’d be close, but no cigar: the earth’s axis, which is tilted at about 23.5 degrees to the plane of the earth’s orbit, is actually not fixed in its direction in space. The earth rotates on an axis which precesses, similar to that of a spinning top with one point fixed. It takes 26,000 years to go al the way around and come back roughly where it was. And so, in fact, the calendar year (also called the “tropical year”) is about 20 minutes shorter than the sidereal year. (You can easily calculate this yourself: it’s 1/26000 of a year!)

Our Gregorian calendar will keep the spring equinox quite close to March 21 or so, but eventually our familiar winter constellations like Orion will eventually become summer ones, and the North Star will appear to move in ever-widening circles about the celestial north pole.

If you dig further into all this you quickly see that the day, which I am sure you’ll find people to tell you is “24 hours” has a similarly ambiguous definition. The sidereal day, the time it takes the earth to spin once on its axis, is 23 hours, 56 min, 4.1 sec., just less than the solar day of 24 hours. Not surprisingly, after you think about it, this difference is close to 1/365 of a day, since as the earth goes around the sun, one full orbit is in effect a day. (If the earth were not rotating, then there would be one solar day per year.)

But is a day even exactly 24 hours? It turns out that for various reasons, the earth’s rotation speeds up and slows down over long periods. The second was redefined in 1967 to be the time it takes for 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. This is the basis for our measurement of time in the SI system of units. As a result, we no longer define the second as 1/86400 of a solar day, and we need to add in a leap second every so often to account for the fact that the earth’s rotation is slowing by about 2.3 milliseconds per day per century, and we chose the year 1900 as the reference for the second. This means we are now accumulating one leap second every 430 days or so. We’ve added leap seconds at about that rate since the first one in 1972 (always at midnight on New Year’s Eve).

So now we have International Atomic Time (TAI) with no leap seconds, and Coordinated Universal Time (UTC) which have drifted apart by 33 seconds since 1972. We need both systems, since we want a simple way to calculate accurate time differences without having to take into account leap seconds, but we want noon to stay when the sun is high in the sky. The US Navy is on it, don’t worry.

we need to add in a leap second every so often to account for the fact that the earth’s rotation is slowing by about 1 second per 500 days.

That can’t be right; we’d have 25-hour days in just 5,000 years. And we’d be doing a leap-second every two weeks by now.

http://nsaunders.wordpress.com Neil

Nice explanation. Except:

Our Gregorian calendar will keep the spring equinox quite close to March 21 or so, but eventually our familiar winter constellations like Orion will eventually become summer ones…

is all reversed for those of us in the southern hemisphere

http://www.ucolick.org/~sla/leapsecs/dutc.html Steve Allen

The rotation is not slowing by one second per 500 days. The atomic second was too short at the time of adoption, by an amount that accumulates to one second in 500 days or so. See the website linked for more.

Now, of course us hard-headed Arizonans don’t really care what the feds say about that changing the clock thing – we’ve got what you northerners call summer all year round anyway. (And did I mention today was 75 degrees?)

Ben

Daylight saving time, originally intended as an energy saving measure, has its origins in two world wars and an oil shock. It’s your patriotic duty. Arizona doesn’t have daylight saving time because we hate freedom. Also because during the summer, the sooner the sun goes down the better.

Leap second decisions are made by the International Earth Rotation Service, a shadowy quasi-governmental organization that keeps the Earth rotating: http://www.iers.org

http://blog.demring.com/ Gorm

Slightly off topic:

How come we haven’t rationalized the calendar already, like the French revolutionaries tried to with their decimal calendar (and clock)? This would make time so much more understandable, reducing the seven scales (sec, min, hour, day, week, month, year) to two: Day and year. This is not just a practical matter, its almost existential!

http://www.cfa.harvard.edu/~dphil/ David

The difference between the solar day and the sidereal day is very convenient when performing experiments looking for couplings of fundamental particles to background fields. In one of our experiments, we search for a coupling of the neutron to a background field, fixed in space by measuring the energy splitting of the ground state of He-3 and Xe-129. We let the experiment sit in the lab, and as a the earth rotates the direction the particles point (as defined by an applied magnetic field) changes with respect to the fixed stars while remaining fixed with respect to earth.

Now, in the presence of a background field coupling to neutrons, these energy levels (and thus the frequency emitted by the experiment) will shift as the earth rotates. However, you might say, “Great at midnight when the outside air temperature is low and there are no cars in the parking lot (for example), the energy levels are small, while at noon, when the world is warmer and there are lots of cars in the parking lot the energy splitting is larger. Why should I think this has anything to do with fundamental physics?”

Well, since the solar day and the sidereal day go in and out of phase over the course of one year, if you wait six months the two will be out of phase. Therefore, if we see a signal that has some phase with respect to the solar day, just wait six months and it should have the opposite phase. Another way to say this is that with a year of data, the Fourier components at the solar and sidereal days are clearly distinguished.

This has enabled us to show that there is no such coupling (to the spin of the neutron) at the 10-31 GeV level. Why do we report this result as a very small fraction of a very large multiple of electron volts? One GeV is approximately the mass of the neutron. A first, crude, guess as to how big an effect we might expect to see if we thought that Lorentz symmetry was broken spontaneously on an energy scale given by some fundamental symmetry might be mneutron2/Mplanck which is 10-19 GeV. Therefore, we have seen no signs of such a field at a level well below first order in the ratio of the mass of the neutron to the Planck mass.

http://www.cfa.harvard.edu/~dphil/ David

Oops. You can see I can’t read the instructions all that well. In the last paragraph, those are 1e-31 GeV and (m_neutron)^2/M_planck and 1e-19 GeV.

http://blogs.discovermagazine.com/cosmicvariance/john John

Very interesting…in my post I seem to have hit upon something here! Perhaps my sentence was not correct. In any case, either

a) the earth’s rotation really is slowing down, and therefore we need to add leap seconds every 500 days or so, or

b) we got the value of the second wrong in 1967 by 1 part in 43,200,000,

or perhaps both?

There is no question that the earth’s rotation is slowing such that the average day is increasing by 2.3 milliseconds per day per century. This is due to tidal braking – that energy has to go somewhere. It means that after 100 years we have a clock that “loses” 1 second every 430 days or so, and needs to be adjusted.

It certainly was not that we got the second wrong…was it? We measured that to 8 digits, right? Or did we? That is, in 1967 did we know the rotational period of the earth to 1 part in 43,200,000? I would have thought so.

This is fascinating, and I confess that my statement that “earth’s rotation is slowing by about 1 second per 500 days” is not accurate. I will repair it in the post to avoid further embarrassment…thanks for keeping me honest.

It is because we chose the year 1900 as the reference for the second.

http://msmith13.wordpress.com Mark

DST is proof that even a forward-thinking creative intellect Like Ben Franklin can have a bonehead idea. It makes no sense at all, a fact which probably insured its adoption.

People are eager to enjoy every extra second of daylight we get in the summer months, but they will be damned if they’ll wake up earlier in order to do it. Since there’s no other way to do it except waking up earlier, you have to give people a plan to follow that obscures that fact. So they hack away at the conventions of time keeping, which is all human created anyway. Now people can pretend that all the extra daylight is tacked on at the end of the day, and they spend that extra time congratulating themselves on their cleverness in divorcing themselves from the bonds of objective reality. So there’s no surprise that the subject is filled with mystery and weirdness.

John Merryman

You would think if the gubment can make the sun set later, they could figure out how to do lots of other things a little better.

On another note, is time the basis of motion, or is it a consequence of motion?

http://www.ucolick.org/~sla/leapsecs/timescales.html Steve Allen

No, John, it’s not because the year 1900 was chosen as the reference for the second. Yes, astronomers believed that and promulgated that idea, but they were wrong. Read the sordid history of time scales in my link for this post carefully, and look at the text of the link in my previous post. The year 1900 was chosen because it corresponded to Newcomb’s tables, which in 1896 had been universally adopted for all national ephemerides starting in 1901. But the observations used by Newcomb covered roughly 1750 to 1892, so their mean corresponded to the length of day around 1820, not 1900.

Studying all of this is an excellent exercise in human cognition, and human foibles, as more and more scientific evidence shattered old beliefs that some things — which were presumed constant in the established models of reality — were not actually constant. This led to several intervals of very confused nomenclature as the paradigm shifted and it became evident that there was a distinction between two different things which were formerly presumed to be one thing.

Polie

You will be excited to learn that even the U.S. station at the geographic south pole switches to daylight savings time, although there is daylight for 6 months and no daylight for 6 months …

Can you point me to the references which discuss Newomb’s tables and all that?

Your point about human cognition and foibles is and excellent one. Thanks again.

You should write a book on this – it’s important!

Jim Clarage

…since 1582 when Pope Gregory introduced the new calendar to keep Easter from drifting, slowly but surely, away from the spring equinox

I don’t think Easter can ever “drift” away from the Spring Equinox. That’s the beauty of its definition. Unlike most holidays Easter is not defined by a fixed calendar date; rather it is defined relative to the Spring Equinox. In ecclesiastical pseudo-code:

Easter = 1st Sunday after the 1st full moon after the Spring Equinox.

where “after” is the inclusive “on or after”.

For example this is why Easter is so early this year. The full moon falls directly on the Spring Equinox. There’s a variance of more than a month built into the holiday from year to year. But it cannot arbitrarily drift from the Equinox (unless by equinox you mean March 21, since obviously what we call March 21 can drift.).

Corrollary, to calculate when to start drinking on Fat Tuesday:

Mardis Gras =
1st Sunday after the 1st full moon after the Spring Equinox

minus 1 week (Passover or Palm Sunday)

minus 1 month (desert fasting and atonement myth/rituals/ceremonies)

minus 1 day (day of Bacchus preceding Ash Wednesday)

http://www.ucolick.org/~sla/leapsecs/timescales.html Steve Allen

Regarding Easter and the equinox it is important to distinguish between the calendar in conventional use and the actual motions of the rocks orbiting the sun. The former aims to match the latter in some respect, but the devil is in the details. For the best online picture of calendars vs. reality see the nice plot from the Canadians, but don’t take the results too seriously. When computing such things over such intervals it is very easy to neglect a subtle effect.

For a discussion of the subtle difference that not even all astronomers recognize between the tropical year (as used to define the length of the second) and the Vernal Equinox year (the one the Gregorian calendar was designed to match), and much else on the topic of calendars and humanity, see Duncan Steel’s masterpiece.

Lawrence B. Crowell

The framing of time with respect to the heavens and seasons is ancient. It is even in the Bible, and in fact is virtually a third ‘creation story’ in the Old Testament. Although it is less obviously displayed, details being spread around the various books, it deserves more attention than it gets, For instance:

1 Samuel 2;8 “For the pillars of the earth are the Lord’s and he hath set the world upon them.”

This is by far the best description of how ‘The Lord’ ‘founded’ the ‘earth’. It is frequently described as a work of ‘surveying’: thus Job is asked

Job 38;4 “Where wast thou when I laid the foundations of the earth?”

38;5 “Who decided the dimensions of it or who stretched the measuring line across it?”

38;6 “Whereupon are the foundations (Hebrew ‘sockets’) thereof fastened, or who laid (Hebrew ‘sank’) the cornerstone?”

These ‘foundations’, ‘the pillars of the earth’, which are set upon ’the waters’, by comparison with other traditions around the world which give more details, can be shown to be the solstices and equinoxes. During Suchot the Lulav and etroge are waved in the six directions, where this is an autumnal “harvest” feast and this signifies the “foundations” or the frame of the world.

Of course we have leaned a bit since then, but this was a sort of mythic idea of there being a coordinate system in the universe, which also marked time.

Lawrence B. Crowell

marc

Daylight time explains global warming!! The following appeared as a letter to the editor in an Arkansas paper:

Daylight exacerbates warning:

“You may have noticed that March of this year was particularly hot. As a matter of fact, I understand that it was the hottest March since the beginning of the last century. All of the trees were fully leafed out and legions of bugs and snakes were crawling around during a time in Arkansas when, on a normal year, we might see a snowflake or two. This should come as no surprise to any reasonable person. As you know, Daylight Saving Time started almost a month early this year. You would think that members of Congress would have considered the warming effect that an extra hour of daylight would have on our climate. Or did they ? Perhaps this is another plot by a liberal Congress to make us believe that global warming is a real threat. Perhaps next time there should be serious studies performed before Congress passes laws with such far-reaching effects.”
CONNIE M. MESKIMEN / Hot Springs

http://www.geocities.com/aletawcox/ Sam Cox

John M said,

“On another note, is time the basis of motion, or is it a consequence of motion?”

Hi John…rather the observation and measurement of motion. The existence of time is a frame of reference phenomenon related to the link between observation and existence themselves…per relativity and QM….

LC,

Really profound. Time is profound as our existence and that of the universe itself, laced with complex information as they are, are profound. Soemtimes we have to resort to poetry and myth to begin to grasp the awesome-ness of it all!

I’m pushing 70 and was updating my scrapbook today…reviewing a life of activities. The grandkids gained a better appreciation of the meaning of their lives as they saw pictures of relatives long dead from the 19th century and related the existence of these folks to that of “grandpop” – and themselves.

Our ancestry is a “tree”…the ancestry of the human race is a “tree”…the ancestry of all living is a “tree”…everything organic and inorganic in the universe is a “tree”. Everything and every event is linked to every other event everywhere. Ultimately, the location of everything stays the same…it is the “size” of measured and observed space and time which separates us. When that “space” and when that “time” are not measured to exist, everything, the entire cosmos is one…at the lowest possible entropy state.

Everything in the universe foundationally depends on everything else…good ecology and good philosophy…”natural philosophy” too.

No. 9

Well, that takes care of time. What do you guys have on newsweek?

For those not old enough to remember the debates on DST, one of the biggest arguments was that it was gov’ment tellin’ people how to run their lives just like them dirty commies do. In Arizona (Barry Goldwater times) this was a major reason for eschewing DST–New Mexico, Texas, Louisiana, etc. are at the same latitude, so the physical logic is the same for them, and all these other states did adopt DST.

The argument that “you can just get up an hour earlier” doesn’t work, because most work schedules mean that the additional time would only be a single hour in the morning, rather than providing a block of time for a more leisurely golf round or watching the kid play baseball. DSL offers several advantages; whether those advantages outweigh the disadvantage of changing your clocks twice a year seems to be an individual decision. My take on John’s post is that he’s pointing out that we have to adjust time to match our perceptions of nature for many other reasons, too. The same sort of arguments as are used against DSL could also be used against writing from left to right across the page, or driving on the right side of the road, or any other social practice that has been instituted. It’s a societal practice, not a scientific one; when in Rome, do as the Romans do.

http://tyrannogenius.blogspot.com Neil B.

It’s been rather well debunked (sorry, don’t have refs) that DST doesn’t really save energy etc. It’s mostly a scam from the tourism industry and business folks who want people out shopping more. DST is a great nuisance, and it is unhealthy to get up very early (studies show that teens are too sleepy in high schools, when they get up for classes starting around 8 am or worse, 7 am by the sun.) Cars are harder to start in the cold, kids stand around in the dark to get school buses, etc. They should shrink DST if have it at all.

John Merryman

Sam,

So motion is real and the frames of reference are the measure. This means the arrow of time for the series of events that is time goes from future potential to past circumstance. It’s a simple point, so why doesn’t physics take into account that as each event is replaced by the next, what is time goes from the future to the past? Instead physics seems to treat time as an actual dimension in which the present is a subjective point of reference, like frames on a film. I’ve brought this up a number of times on CV, but it doesn’t draw much response. You would think that if it was wrong, someone would have explained why. If it’s right, I’d think there would be some interest in considering it.

Kaleberg

I thought the purpose of daylight savings time was to save the poor sun which gets really weak every winter having lit things up for us and kept us warm all summer. Every fall we change the clock and, if we are working like most good Americans, we don’t see the sun again until springtime. By sparing the sun the effort of having to provide heat and warmth for us, and relying on artificial energy sources instead, we make it more likely that it will recover from its winter-time weakness.

jimvj

So why do months have their weird pattern of days?
Why not option 1 below in which Feb has 30/31 days;
or the more aesthetic almost periodic option?

(studies show that teens are too sleepy in high schools, when they get up for classes starting around 8 am or worse, 7 am by the sun.)

And it must be the DST, and not the teens’ social lives and avoidance of sensible bed times, that is responsible.

Anyone opposed to DST is welcome to come babysit for us: our child wakes up at first light, which is 5:30 in the middle of summer, but would be 4:30 without DST.

rillian

My favorite pattern is 12 30-day months plus 5 extra days before the new year (6 on leap years). Another variation is 13*28 days plus 1 or 2 extra holidays.

Anyone have a scheme based on powers of 10 and seconds? Kiloseconds are fun for intervals, but as an absolute system the numbers get too big, even setting aside the lack of reference to noon and dusk. The best “metric” scheme I’ve seen is the more recent year.day-of-year.milliday where milliday is the . That unnecessarily moves the meridian though.

bipolar2

Gee, futureman. Bet you could get further “inspiration” from A.N. Whitehead.
Process and Reality.

http://lablemminglounge.blogspot.com/ Lab Lemming

An additional benefit of being forced to get up before dawn in early March is that you get to see Mercury.

http://www.geocities.com/aletawcox/ Sam Cox

Hi John,

I think everybody is thinking about the possible implications of CPT symmetry insofar as the macroscopic universe is concerned. I also think that the fact that time even seems to have a different quality than the other spatial dimensions implies that there is something unique about it…in spite of the fact that treating time as space-like in relativity works just fine.

Remember, we can find the “Big Bang” at a certain place in scale…and locate the “Big Crunch” too…to say nothing of the fact that every second of a stars existence from beginning to end could be observed from some coordinates elsewhere in the cosmos. To me all this implies that time really is not absolute (as Einstein obviously asserted) but that time “happens” when we take a frame of reference and electromagnetically observe the universe of stored information in a certain very specific way.

However, we observe and measure time (along with space) and therefore we ARE justified in assuming that the universe is not, nor can be completely static. However we are also justified in concluding that time does not exist cosmologically as we humans individually or collectively measure it. Mass and energy density presence in the universe defines both time and space, not the other way around.

I don’t think we can justifiably assume that each event is “replaced by the next”, to use your words, when we can look at a planet orbiting a star 10 light years away, and see events which transpired 10 years ago as if they were happening today. The only conclusion we CAN draw is that everything which exists and “happens” in the universe has an eternal place, or set of coordinates.

I think you may be rushing to conclusions about time which are not justified by field evidence. This universe of ours is really a counterintuitive place…things are, to use the poets words, “not as they seem”.

Best Wishes…Sam

Ray

It is not ‘daylight-savings” Time.
It is Daylight Saving Time.

Accurate-to-the-second time and date only work well locally, so time zones were invented to standardize. Prior to railroads, each community kept local solar time, which was reasonably accurate but dependent on longitude and only pertinent locally.

For example: A train might leave Chicago at 1pm local Chicago time, and travel east for 1 hour at 96mph. It would arrive at a South Bend at 2pm Chicago time, but that would be somewhat later, local South Bend time, say 2:10. Today, you reset your watch when you cross time zones. Without time zones, you would reset it some weird amount every time you traveled east or west. You would only know what the new local time was by asking – or being a scientist with a sextant.

With time zones the times are predictable, even if there is the element of arbitrary fiat.
If South Bend were EST and Chicago CST, the train would leave Chicago at 1pm CST and arrive in South Bend (1 hour later) at 3pm EST. If both were in the same time zone, it would arrive (1 hour later) at 2pm. Establishing time zones made life much easier for transportation and communication.

http://lablemminglounge.blogspot.com/ Lab Lemming

“Without time zones, you would reset it some weird amount every time you traveled east or west. You would only know what the new local time was by asking – or being a scientist with a sextant.”

Or a wireless connection, or a Blackberry, or an iPhone, or…

Old is the new new.

John Merryman

Sam,

I realize it is normal to model time as linear. That’s what history is. Still, two points in time don’t co-exist the way two points in space can. The light we see was radiated ten years ago and crossed an enormous amount of space. Because energy is conserved, it can’t physically exist in previous states.

My point about time is that it is specifically a consequence of motion. It would be equally meaningless to say that everything exists at the point of the present, because, according to the uncertainty principle, position and momentum are not compatible, measurement wise. So if time is a function of momentum, it would cease to exist at a point. Just as temperature ceases to exist at the absolute, motionless state.
I think the reason we process it as a point is because our brains must process information as frames, otherwise it would all blur together.

The further question though, is space. We define it according to motion of energy and mass. but does motion create it, like time and temperature? Say there was no motion. Would energy/mass exist? A non-flucuating vacuum? There would be no geometry, no math, no physics, no equations. Just void…. Is space the void? The non-being to the being of mass/energy? As zero is to one? I think time is a description of motion, but I’m not so sure about space.
Consider one of my earlier points; That as the universe expands, according to redshift, the speed of light remains stable. This would make the expanding universe an increasing volume of stable space, rather then expanding space. Not that the speed of light couldn’t vary, but we wouldn’t have the yardstick to detect it. Whole other argument there though.
So space is the real mystery to me. Getting our hands around that would be like understanding death, but we’d probably just lose a few fingers trying. Getting out past the tattered edges of reality and you just come back tattered, if at all. The whole being and non-being thing.

Time is “linear” as space is “flat”. We take a 4D frame of reference and define everything around that frame of reference. So long as other folks share a similar frame of reference, we come to the same (or similar) conclusions about reality.

However we are trying to establish the nature of cosmological reality, and the idea that one event “replaces another” doesn’t match the overall situation.
Rather, one event replaces the other as WE observe time and space at our coordinates.

Be careful not to down play the observation with distance factor I refer to- it is significant. We exist- the universe we exist in, exists because of that factor. It is not a matter of “diminishing photons”, (though there are interesting clues in that phenomenon) rather separation in what we observe as space and time. There may be a supernova out there 1,000 light years away which has already occurred, yet we have not yet been destroyed by it….

John Merryman

Sam,

Is there such a thing as an objective perspective, Tegemark’s bird’s eye view? Or is that an oxymoron? The problem with defining space as three dimensional is that these serve as coordinates for the center point. While we as individuals effectively function as points in space(and time), they are not the same point. Although much of politics and religion revolves around providing such a communal point, sects based on different points emerge, resulting in large scale conflict. You might say the Arabs and the Israelis use different frames of reference to define the same space (and time).

I’m certainly not playing down how distance regulates energy transfer. If the blast of a super nova from 1000 years ago is set to destroy us, it will do so because the energy blasted in our direction reaches us and is no longer contained in the original star. As I’ve argued, there is only energy, spread across space. Time, like temperature, is a measure of the motion of this activity. This isn’t presentism, because as a measure of motion it would be meaningless to specify that all this activity exists at the same instant in time. We can model time as a tensor, just as we measure temperature as a scalar, but there is no fundamental existance of this dimension, any more then there is a fundamental temperature scale. The only absolute for both would be the complete absence of motion. Time may seem fundamental from our perspective, but so is temperature. Consider the basis of Big Bang theory, redshift and cosmic background radiation, are both measures of temperature, ie. reduced levels of energy from what the scale would otherwise be. We cannot travel back in time to see what happened, we can only measure current energy levels.

<boring quibble> Tommaso, you talk as though the solar day was fixed at 24 hours (apart from the odd millisecond here and there) … actually it is the sidereal day that is pretty much fixed (at 23h 56m 4.1s)owing to conservation of angular momentum – the solar day is sometimes longer than 24h & sometimes shorter as the sun does not move exactly 360/365.2422 degrees a day relative to the stellar background owing to the ellipticity of our orbit </boring quibble>

http://www.cgoakley.demon.co.uk/qft/ Chris Oakley

Oh sorry – getting confused: I meant John not Tommaso … the cumulative difference between actual & mean solar day adds up to quite a lot (+/- 15 minutes) & is a correction one needs to apply to sundial readings (although I believe that it is no longer common practise to rely on these for timekeeping).